Analysis and Approaches for IBDP Maths Ebook 2 | Page 197

Exercise 60
1. The region R is enclosed by the graph of
the x -axis. Find the area of R .
y�e
2x
� 1, the graph of x y e
2. The region R is enclosed by the graph of y�
2ln x, the graph of
6
� � � 2� 0 and
2 2
4x e y 8e
0
� � � and
the x -axis. Find the volume of the solid of revolution formed when R is rotated through
2π about the x -axis.
[7]
[7]
13
�
3. The region R is enclosed by the graph of y � 5 x , the graph of y�25x� 75 and the
y -axis. Find the area of R .
[8]
1
2
4. The region R is enclosed by the graph of y � x� 1, the graph of y� ( x� 4) � 3 and
2
2
the y -axis. The domain of y� ( x� 4) � 3 is { x: x� 4} . Find the volume of the solid of
revolution formed when R is rotated through 2π about the y -axis.
[9]
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